The men, aged between 19 and 55, were arrested for a public order offense.
A video posted on social media this week shows the group holding a cardboard model of the 24-storey apartment block, which went up in flames in June of previous year, killing 72 people.
Ms Connell told The Sun: "I had no idea they were handing themselves in".
One person shouts "jump out the window" while another offers the original fire brigade advice before the scale of the tragedy was understood, saying "stay in your flats". "It's like killing these poor people all over again".
Grenfell United, the official organisation for bereaved, survivors and community of Grenfell Tower, said: "It's a disgusting video".
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Khadijah Mamudu, whose mother and younger brother escaped the June 14, 2017, firestorm, called the burning of the model a "vile act".
"Not only is it extremely upsetting to survivors & people who lost family, it's hateful & offensive to everyone that has been affected by the tragic events of that night", the group said.
"Help me, help me", another man says, mimicking distressed screams. Raucous laughter can be heard. "We will continue to investigate and where appropriate prosecute anyone who is financially profiting from the Grenfell fire, and taking away resources and support for the true victims".
Another voice can be heard saying "that's what happens when they don't pay their rent".
The video ends as the model is completely consumed by the fire, with one bystander saying: "Perfect".
As the video was circulating on Twitter, a number of people condemned the act. In the background, a St. George's flag can be seen. By Monday evening, the video was trending in Britain, with thousands expressing shock and disbelief at the insensitivity of the group in the recording.
A video has emerged on social media showing a group laughing at the victims of the fire tragedy while burning a cardboard model.